Problem: Simplify the following expression: $\sqrt{27} + \sqrt{3}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{27} + \sqrt{3}$ $= \sqrt{9 \cdot 3} + \sqrt{3}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{3} + \sqrt{3}$ $= 3\sqrt{3} + \sqrt{3}$ Finally, simplify by combining the terms. $= ( 3 + 1 )\sqrt{3} = 4\sqrt{3}$